CN103528840A - Modulation transfer function measurement method on basis of characteristics of detector of X-ray imaging system - Google Patents

Abstract

The invention belongs to the field of biomedical engineering and a computer and relates to a modulation transfer function measurement method on the basis of the characteristics of a detector of an X-ray imaging system. The modulation transfer function measurement method comprises the following steps of: placing a knife edge testing instrument to enable the knife edge testing instrument to be clung to the detector, enabling an inclination angle to be formed between a knife edge and the sampling direction of the detector and continuously acquiring a plurality of images; carrying out superposition averaging on a plurality of knife edge images, reducing system noise and then carrying out knife edge boundary detection on an averaged knife edge image to obtain a knife edge boundary line; carrying out Hough transform on a knife edge boundary line graph to obtain a knife edge inclination angle alpha and establishing an oversampling ESF (Extended Superframe Format) curve; using a C spline as a regression spline f for carrying out segmentation fitting on the oversampling ESF curve; carrying out differential operation to obtain a line spread function; carrying out Fourier transform on the line spread function and then carrying out modulus acquisition to obtain a modulation transfer function; and carrying out normalization processing. The modulation transfer function measurement method solves the problem of fitting error generated when the oversampling ESF curve is acquired by a knife edge method; and compared with a conventional knife edge measurement method, the modulation transfer function measurement method can obtain a more accurate MTF (Modulation Transfer Function) curve.

Description

Modulation transfer function measurement method based on x-ray imaging system detector characteristic

Affiliated technical field

The invention belongs to biomedical engineering and computer realm, relate to a kind of accurate new method of measuring of modulation transfer function of digital X-ray imaging system.

Background technology

Modulation transfer function (Modulation Transfer Function, MTF) is the transport function of degree of modulation, is the quantitative description to linear image system space frequency transmission characteristic, is the impressive progress in image evaluation method.Generally use before this qualitative description index, such as image density, contrast, sharpness, resolution and degree of distortion etc. evaluated the quality of image of imaging system, but its result is affected greatly by factor and individual subjective factor.With digital X-ray imaging technology, develop rapidly in recent years, MTF has become as objective indicator the important image evaluation means that radiophotography worker and researcher pay close attention to.Meanwhile, MTF is also the necessary parameter that obtains imaging system detective quantum efficiency.

To evaluate quantitatively the intrinsic image quality of digital X-ray imaging system, only need to calculate the intrinsic pre-sampling MTF of system that not affected by factor and individual subjective factor.In reality, system MTF is often calculated by following three kinds of spread functions: point spread function, line spread function and edge response function, they describe respectively point, line and edge disperse degree after imaging system, can indirectly reflect system imaging ability.

Measure in the method for MTF at present, line can obtain high-precision mtf value to chucking method, but line can only provide the mtf value of limited several integer space frequency locations to chucking method, cannot realize the comprehensive assessment of ssystem transfer function.In order to obtain the MTF change curve under imaging system spatial frequency range, general conventional measuring method comprises slit method and knife-edge method, it is the better method that obtains MTF that slit method (Slit Camera) and knife-edge method (Edge) Yi Bei International Society of Radiology are known as, Japan is defined as slit method the standard method of measuring MTF, and knife-edge method Ye Yibei International Electrotechnical Commission (I.E.C.) (IEC) is appointed as the standard method of measuring system MTF.When under the same system obtaining by slit method and knife-edge method, different MTF curves compare, known the former has compared with high s/n ratio at high-frequency domain, and the latter has compared with high s/n ratio at lower frequency region.The system MTF obtaining by slit method is accurate, and easy and simple to handle, method is ripe.But because of its difficulty of processing high (slit width is less than or equal to 10 microns, and error is in 1 micron), cause the more difficult quilt of this method in actual applications to be promoted.Because knife-edge method surveying instrument is relatively easy from processing, in scientific experiment and conventional sense, use comparatively extensive.

Adopt knife-edge method can obtain edge-spread function (the Edge Spread Function of the metal module edge of a knife, ESF), it has reflected through imaging system back edge disperse degree, the derivative of ESF is line spread function (Line Spread Function, LSF), through Fourier transform, can obtain system MTF again, most of research about MTF at present all launches based on knife-edge method technology.

In order to obtain high-resolution MTF curve, generally adopt at present improved MTF edge of a knife measuring method, be about to edge of a knife direction and image sampling direction angled, with this, obtain the edge response function ESF of over-sampling, then by Fourier transform, obtain high-resolution MTF curve.Due to obtaining by ESF differentiate is realized of LSF curve, the noise in ESF curve is amplified by differentiate process, has hindered the accurate extraction of LSF curve.In order to overcome this difficulty, the accuracy that existing scholar's expectation is extracted by the methods such as ESF curve Gaussian smoothing, multistage sectional curve matching, monotonicity curve being improved to LSF curve at present.But up to the present,, because said method does not make full use of the priori of detector nature, aspect MTF Evaluation accuracy and robustness, still there is larger shortcoming.

Therefore, explore a kind of effective MTF edge of a knife measuring method, make full use of the priori of detector itself, improve knife-edge method MTF measuring accuracy, accurately realize the modulation transfer function characteristic evaluation of digital X-ray imaging system, become the research emphasis of imaging system Performance Evaluation, this development and application tool for imaging system is of great significance.

Summary of the invention

Purport of the present invention is the above-mentioned deficiency that overcomes prior art, a kind of modulation transfer function new method of measuring of digital X-ray imaging system is provided, with this, solve the basic problem in digital radiation imaging system Performance Evaluation: realize the Measurement accuracy of the modulation transfer function of digital X-ray imaging system, for further comprehensive assessment radiologicaal imaging system performance provides strong condition.Technical scheme of the present invention is as follows:

A modulation transfer function measurement method based on x-ray imaging system detector characteristic, comprises the following steps:

1. the exposure parameter of digital radiation imaging system is set, places edge of a knife testing tool and be close to detector, and make the edge of a knife and detector sample direction have an angle of inclination, continuous acquisition multiple image;

2. to several edge of a knife image superposed averages, reduce system noise, then the edge of a knife image after average is carried out to edge of a knife Boundary Detection, and utilize fitting a straight line to obtain edge of a knife boundary straight line;

3. edge of a knife boundary straight line figure is carried out to Hough conversion, obtain edge of a knife tilt angle alpha, then according to formula N=round (1/tan α), obtain interpolation corresponding to this inclination angle and count N, build over-sampling ESF curve, round symbology bracket function;

4. adopt C SPL, as returning SPL f, ESF curve is carried out to piece wise least square method matching, meet constraint condition simultaneously, be i.e. during matching, guarantee that ESF curve left-half is monotone nondecreasing concave function, right half part is monotone nondecreasing convex function;

5. the ESF curve through least square fitting is carried out to calculus of differences and obtain line spread function LSF (x);

6. line spread function LSF (x) is carried out to Fourier transform delivery again, obtain modulation transfer function ' (f);

7. to MTF ', (f) adopt zero frequency position mtf value to be normalized, obtain normalized modulation transfer function (f).

As preferred implementation, step 4. in, adopt 3 rank C SPL as recurrence SPL f, ESF curve is carried out to piecewise fitting, satisfied constraint condition is: f ' (x) >=0, $\left\{\begin{array}{cc}{f}^{\″}\left(x\right)\≥0,& x\∈[x_{\min },x_{\mathrm{mid}}]\\ f^{\″}\left(x\right)\≥0,& x\∈[x_{\mathrm{mid}},x_{\max }]\end{array}\right.,$ Here f ' (x) and f ' ' (x) be respectively first order derivative and the second derivative that returns SPL f, x _min, x _midand x _maxrespectively the left end point for the treatment of matching ESF curve, border, center and right endpoint, λ is smoothing factor, λ>=0, for controlling the smoothness of curve and the balance between error.

When the modulation transfer function that carries out digital X-ray imaging system is measured, by the modulation transfer function new method of measuring based on x-ray imaging system detector characteristic of the present invention, solve error of fitting problem when knife-edge method obtains over-sampling ESF curve, can obtain more traditional edge of a knife measuring method MTF curve more accurately.The application of the method, will be accurate measuring system modulation transfer function, and Efficient Evaluation radiologicaal imaging system performance provides and provides powerful support for.

Accompanying drawing explanation

Fig. 1 .8 bar interpolation reconstruction over-sampling ESF curve.

Fig. 2. the X-ray imaging results mean chart of knife-edge method testing tool.

Fig. 3. the edge of a knife boundary straight line fitting result of knife-edge method testing tool.

Fig. 4. the LSF curve comparison that the inventive method and current 3 kinds of methods obtain.

Fig. 5. the variance contrast of 15 LSF curves that the inventive method and current 3 kinds of methods obtain.

Fig. 6. the MTF curve comparison that the inventive method and current 3 kinds of methods obtain.

The MTF variance curve contrast that Fig. 7 the inventive method and current 3 kinds of methods obtain.

The LSF curve that Fig. 8 .4 kind method obtains and true LSF curve comparison.

The MTF curve that Fig. 9 .4 kind method obtains and true MTF curve comparison.

The MTF graph of errors that Figure 10 .4 kind method obtains.

Embodiment

Error of fitting problem while obtaining over-sampling ESF curve for traditional knife-edge method, the present invention proposes the modulation transfer function new method of measuring based on x-ray imaging system detector characteristic, by the C spline curve fitting method of fusion detection device characteristic priori, with this, build over-sampling ESF curve accurately, finally can obtain more traditional edge of a knife measuring method MTF curve more accurately.Below the present invention is described in detail.

1ESF over-sampling curve acquisition and processing

Utilize oversampling technique reconstruct ESF, the edge of a knife need be become certain inclination angle put with detector matrix, conventionally inclination alpha between instrument edge and digital detector array direction is remained 1.5 °～7.1 ° (corresponding interpolation number is 8～38), the resolution of α less (interpolation number is higher) the MTF curve that obtains is just higher, but noise in corresponding MTF curve is also larger.

For edge of a knife angle of inclination, be 7.1 °, for this inclination angle, expect that accurate edge response function ESF must carry out 8 interpolation near the image edge of a knife.The relation at interpolation number and angle of inclination is determined by formula below

N _ave＝1/tanα (1)

Because interpolation number corresponding to actual edge of a knife angle of inclination is not generally integer, in the measuring method before therefore, generally get and approach interpolation most and count N _aveinteger N

N＝round(N _ave)＝round(1/tanα) (2)

Round symbology bracket function in above formula (2).

Adopt 8 interpolation to come the reconstruct over-sampling ESF curve can be with reference to numerical order in Fig. 1, corresponding interpolation sequence from 1 to 8, then from 9 to 16, the rest may be inferred completes the reconstruct of whole piece ESF curve, obtains ESF (x).

Want to obtain line spread function LSF (x) from edge response function ESF (x) computing, to ESF (x) carry out calculus of differences or use convolution filter [0.5,0,0.5] all can,

LSF(x)＝dESF(x)/dx (3)

LSF (x) function delivery again after Fourier transform, just can obtain its modulation transfer function

MTF′(f)＝|FT(LSF(x))| (4)

In formula, FT is Fourier transform, conventionally when descriptive system modulation transfer function, uses the result of normalized, and its formula is

$\mathrm{MTF}\left(f\right)=\frac{{\mathrm{MTF}}^{\′}\left(f\right)}{{\mathrm{MTF}}^{\′}\left(f\right){|}_{f=0}}---\left(5\right)$

In general, the contrast of modulation transfer function lower frequency region major decision image, high-frequency domain determines reproduction ability and edge's sharpness of image detail.From MTF envelope of curves area, can judge system imaging quality good or not, conventionally wish that the area that imaging system MTF curve comprises is the bigger the better.

Because MTF measuring accuracy is subject to the restriction of the noise in over-sampling ESF curve, the over-sampling ESF curve that need to obtain knife-edge method be processed, and existing scholar has proposed several disposal routes at present.Samei proposed the noise that a kind of level and smooth method of Gauss's weighting reduces ESF curve, and Samei and Saunders have proposed again the precision that quadravalence moving curve approximating method has improved MTF HFS afterwards.Maidment and Albert has proposed to utilize the monotonicity of ESF curve self to realize the method for curve and noise reduction, has obtained certain effect.But up to the present,, because said method does not make full use of the priori of detector nature, aspect MTF Evaluation accuracy and robustness, also has larger shortcoming.The present invention is in order to improve MTF measuring accuracy, modulation transfer function new method of measuring based on x-ray imaging system detector characteristic has been proposed, by 3 rank C batten piecewise fittings, the priori of fusion detection device characteristic, obtain ESF fitting result accurately, then calculate and obtain MTF curve.

The 2 ESF curves that merge based on detector priori

In order to extract the priori of detector characteristic, can consider from two kinds of measuring methods of MTF, i.e. knife-edge method and slit method.By the imaging of tool setting jaws equipment, from the brass sheet overlay area of edge of a knife equipment to air section imaging area, X ray intensity in transmission strengthens gradually, and therefore, the cross-section curve of the edge of a knife image finally obtaining (ESF curve) is a monotone nondecreasing curve.Investigate again slit method, by to the imaging of slit equipment, the xsect that can obtain slit image is line diffusion profile (LSF), because slit equipment is from left to right followed successively by brass sheet overlay area, air slots, brass sheet overlay area, therefore, X ray intensity in transmission is the strongest in air slots central authorities, and backward both sides reduce gradually, this has just formed the characteristic of LSF curve: LSF curve left-half is monotone nondecreasing curve, and its right half part is dull non-increasing curve.Because LSF curve is the first order derivative result of ESF curve, therefore, can derive corresponding ESF Curve Property from LSF curve,, centered by edge of a knife border, ESF curve left-half is convex curve, and its right half part is concave curve.Obtain thus, the ESF curve directly related with detector characteristic is to consist of the convex curve of left-half monotone nondecreasing and the concave curve of right half part monotone nondecreasing.

For above-mentioned detector priori is fused in MTF measuring method, we have adopted constraint spline regression method to realize this goal.Constraint spline regression is a kind of distribution-free regression procedure, and it provides effective estimation of regression function and has not needed to provide hypothesis parametric form.The method not only possesses sufficient adaptability, and allows local effect to change, and a kind of effective framework that merges shape constraining is provided.

Given first over-sampling ESF curve model, the some yi in xi position on curve can express by following expression:

y _i＝f(x _i)+ε _i (5)

Curve location coordinate meets x ₁< x ₂< ... x _n, ε _ifor measuring the error between ESF curve and true ESF curve.For the ESF curve that comprises more noise, consider that shape constraining and curve smoothing can obtain more preferably ESF curve-fitting results simultaneously, under recurrence SPL f, minimize following expression formula

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{[y_i-f\left(x_i\right)]}^2+\mathrm{\&lambda;}{\&Integral;}_a^b{\left[f^{\left(k\right)}\left(x\right)\right]}^2\mathrm{dx}---\left(6\right)$

Meet constraint condition: f ' (x) >=0 simultaneously, $\left\{\begin{array}{cc}{f}^{\&Prime;}\left(x\right)\&GreaterEqual;0,& x\&Element;[x_{\min },x_{\mathrm{mid}}]\\ f^{\&Prime;}\left(x\right)\&GreaterEqual;0,& x\&Element;[x_{\mathrm{mid}},x_{\max }]\end{array}\right.,$ Here f ' (x) and f ' ' (x) be respectively first order derivative and the second derivative that returns SPL f, x _min, x _midand x _maxrespectively the left end point for the treatment of matching ESF curve, border, center and right endpoint.

λ in above formula (6) is smoothing factor, and λ >=0, for controlling the smoothness of curve and the balance between error.The present invention adopts cross validation method to obtain the optimal smoothing factor.Parameter k represents the exponent number of splines.Consider that three rank battens have good adaptability, and the fast rise section in can matched curve, so we adopt 3 rank battens to realize minimizing of formula (6).

Returning SPL can adopt the multi-form basis function of several classes to build.B batten is a kind of conventional SPL basis function, possesses substantivity and the recursive definition of structure.Other basis functions comprise and block power function, M batten, C batten etc.The present invention is in order to incorporate the monotonicity of ESF curve and concavity and convexity in MTF measuring method, and we select to adopt C batten to build recurrence SPL as basis function.C batten is the quadratic integral of M SPL, given first M SPL expression formula.

For the recurrence SPL on k rank, givenly treat that the node location of matched curve is x ₁=t ₁=... t _k< ... < t _l+k=...=t _l+2k=x _n, at given curve section t _i≤ x≤t _i+kin, the expression formula of single order M SPL is as follows:

From single order M batten, can obtain k rank M SPL, expression formula is as follows

By to M SPL functional integration, can obtain k rank I SPL

i＝1，…，l+k，x∈[x ₁，x _n] (9)

To k rank I SPL integration, obtain k rank C SPL

i＝1，…，l+k，x∈[x ₁，x _n] (10)

The present invention gets 3 rank C SPL as the recurrence SPL f in formula (6), and ESF curve is carried out to piecewise fitting, thereby obtains high-resolution accurate ESF curve, reduces thus the error of system MTF assessment.

Said process can be summarized as: adopt C SPL, as returning SPL f, over-sampling ESF curve is carried out to piece wise least square method matching, meet constraint condition simultaneously, while being matching, guarantee that ESF curve left-half is monotone nondecreasing concave function, right half part is monotone nondecreasing convex function.

3 modulation transfer function new method of measuring flow processs based on x-ray imaging system detector characteristic

The invention belongs to biomedical engineering and computer realm, relate to a kind of accurate new method of measuring of modulation transfer function of digital X-ray imaging system, its techniqueflow is as follows:

1. the exposure parameter of digital radiation imaging system is set, places edge of a knife testing tool and be close to detector, and make the edge of a knife and detector sample direction have an angle of inclination, continuous acquisition 15 width images;

2. to 15 width edge of a knife image superposed averages, reduce system noise, then the edge of a knife image after average is carried out to edge of a knife Boundary Detection, and utilize fitting a straight line to obtain edge of a knife boundary straight line;

3. edge of a knife boundary straight line figure is carried out to Hough conversion, obtain edge of a knife tilt angle alpha, then according to formula N=round (N _ave)=round (1/tan α) obtains interpolation corresponding to this inclination angle and counts N, thereby constructs over-sampling ESF curve, round symbology bracket function.

4. adopt C SPL, as returning SPL f, over-sampling ESF curve is carried out to piece wise least square method matching, meet constraint condition simultaneously, be i.e. during matching, guarantee that ESF curve left-half is monotone nondecreasing concave function, right half part is monotone nondecreasing convex function.

5. according to formula LSF (x)=dERF (x)/dx, ESF curve is carried out to calculus of differences and obtain line spread function LSF (x);

6. to line spread function LSF (x) carry out Fourier transform again delivery MTF ' (f)=| FT (LSF (x)) |, obtain its modulation transfer function ' (f), then to MTF ', (f) adopt zero frequency position mtf value to be normalized, MTF (f)=MTF ' (f)/MTF ' (f) | _f=0, finally obtain normalization modulation transfer function (f).

The Pixarray100 toy digital radiation imaging system that the present invention adopts U.S. BIOPTICS company to produce.The standard of formulating according to International Electrotechnical Commission (I.E.C.) (IEC) obtains knife-edge method testing tool after the processing of micro-nano equipment, and testing tool is formed by the brass sheet edge of a knife and organic glass bracket assembled, and edge of a knife test material is settled and is fixed on support.In experiment, need the edge of a knife after retrofit to be positioned over field of view center, and make the edge of a knife and detector sample direction have an angle of inclination.

The exposure parameter of digital radiation imaging system is set, edge of a knife testing tool is close to detector, continuous acquisition 15 width images, average these images, can obtain the edge of a knife image shown in Fig. 2.Detect edge of a knife border, and utilize fitting a straight line to obtain edge of a knife boundary straight line, as shown in Figure 3, then by Hough, convert the angle of inclination that can obtain the edge of a knife.

According to edge of a knife angle of inclination, we can obtain the integer interpolation number of traditional edge of a knife measuring method, according to the described method of 5.1 joint, obtain over-sampling ESF primary curve again, and post-sampling the inventive method is processed original ESF curve, for the useful presentation of results of the inventive method is described, we have provided the result contrast of the inventive method with three kinds of methods that adopt at present.

The averaged curve result of 15 LSF curves that Fig. 4 has provided and adopted that Gauss's weighting is level and smooth, 4 rank moving curve matchings, monotone nondecreasing matching and C spline curve fitting method based on x-ray imaging system detector characteristic of the present invention obtain.

For to LSF result accurate evaluation, we have provided the LSF variance curve of 4 kinds of methods, and result as shown in Figure 5, can find out, the LSF curve that the inventive method obtains has minimum variance, have best LSF in 4 kinds of methods again and extract performance.

Fig. 6 has provided 4 kinds of average normalization MTF results that method is corresponding.In cutoff frequency, the relative error of 4 kinds of methods is less than 0.5%, and in sample frequency, the relative error of 4 kinds of methods is less than 0.9%.This has also illustrated that the whole bag of tricks of current sampling is that effectively difference only exists the height with measuring accuracy in MTF measures.

For the MTF curve that 4 kinds of methods are obtained, assess contrast, Fig. 7 has provided the MTF curve relative variance curve that each method obtains.Within the scope of sample frequency 0-10mm-1, the average relative variance of Gauss's weighting smoothing method is 2.01%, the average relative variance of 4 rank moving curve approximating methods is 1.65%, and the average relative variance of monotone nondecreasing matching is 4.29%, and the average relative variance of the inventive method is only 0.83%.The inventive method can reduce the uncertainty (reducing MTF curve variance) of MTF measurement result as can be seen here.

For the accurate performance that further assessment the inventive method is measured at MTF, we test the simulation edge of a knife image of known MTF, and simulation edge of a knife image adopts current this area universally recognized exponential model edge of a knife image, i.e. Lorentzian type function:

$\mathrm{MTF}\left(u\right)=\frac{r^2}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000390311830000011.png,HDA0000390311830000032.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+{(2\mathrm{\&pi;}\&CenterDot;u)}^2}---\left(11\right)$

The r value is here chosen the inverse of detector pixel, and u is spatial frequency.The MTF that specifically can deliver with reference to people such as Esamei measures relevant paper.

Fig. 8 has provided by the LSF curve of 4 kinds of methods acquisitions and the comparison diagram of true LSF curve.Fig. 9 provides the MTF curve of corresponding 4 kinds of methods acquisition and the comparison diagram of true MTF curve, in zero frequency, arrive within the scope of cutoff frequency, between the MTF measurement result that employing Gauss method of weighting obtains and true MTF, average error is 0.65% ± 0.40%, adopt 4 rank gliding smoothing curves, the average error of obtaining MTF is 0.19% ± 0.14%, and adopt dull approximating method, MTF error, be 0.16% ± 0.10%.Adopt the C spline curve fitting method merging based on detector characteristic priori of the present invention, MTF error is 0.12% ± 0.10%.Concrete graph of errors as shown in figure 10, can find out, other 3 kinds of methods that the inventive method adopts at present in MTF measuring accuracy have more advantage.

Net result shows, when the modulation transfer function that carries out digital X-ray imaging system is measured, by the modulation transfer function new method of measuring based on x-ray imaging system detector characteristic of the present invention, take full advantage of monotonicity and the concavity and convexity of detector ESF curve, can obtain more traditional edge of a knife measuring method MTF curve more accurately.The application of the method, will be accurate measuring system modulation transfer function, and Efficient Evaluation radiologicaal imaging system performance provides and provides powerful support for.

Claims (2)

1. the modulation transfer function measurement method based on x-ray imaging system detector characteristic, comprises the following steps:

1. the exposure parameter of digital radiation imaging system is set, places edge of a knife testing tool and be close to detector, and make the edge of a knife and detector sample direction have an angle of inclination, continuous acquisition multiple image;

2. to several edge of a knife image superposed averages, reduce system noise, then the edge of a knife image after average is carried out to edge of a knife Boundary Detection, and utilize fitting a straight line to obtain edge of a knife boundary straight line;

3. edge of a knife boundary straight line figure is carried out to Hough conversion, obtain edge of a knife tilt angle alpha, then according to formula N=round (1/tan α), obtain interpolation corresponding to this inclination angle and count N, build over-sampling ESF curve, round symbology bracket function;

4. adopt C SPL, as returning SPL f, ESF curve is carried out to piece wise least square method matching, meet constraint condition simultaneously, be i.e. during matching, guarantee that ESF curve left-half is monotone nondecreasing concave function, right half part is monotone nondecreasing convex function;

5. the ESF curve through least square fitting is carried out to calculus of differences and obtain line spread function LSF (x);

6. line spread function LSF (x) is carried out to Fourier transform delivery again, obtain modulation transfer function ' (f);

7. to MTF ', (f) adopt zero frequency position mtf value to be normalized, obtain normalized modulation transfer function (f).

2. measuring method according to claim 1, is characterized in that, step 4. in, adopt 3 rank C SPL as recurrence SPL f, ESF curve is carried out to piecewise fitting, satisfied constraint condition is: f ' (x) >=0, $\left\{\begin{array}{cc}{f}^{\&Prime;}\left(x\right)\&GreaterEqual;0,& x\&Element;[x_{\min },x_{\mathrm{mid}}]\\ f^{\&Prime;}\left(x\right)\&GreaterEqual;0,& x\&Element;[x_{\mathrm{mid}},x_{\max }]\end{array}\right.,$ Here f ' (x) and f ' ' (x) be respectively first order derivative and the second derivative that returns SPL f, x _min, x _midand x _maxrespectively the left end point for the treatment of matching ESF curve, border, center and right endpoint,

λ is smoothing factor, and λ >=0, for controlling the smoothness of curve and the balance between error.

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